# Active Willis metamaterials for ultra-compact non-reciprocal linear acoustic devices

## TL;DR

This paper demonstrates experimentally that active Willis metamaterials can achieve highly non-reciprocal sound transport in ultra-compact structures, surpassing passive limitations and enabling advanced sound control and imaging applications.

## Contribution

It introduces an experimental method to create and characterize active Willis metamaterials with independently tunable Willis coupling terms, enabling unprecedented non-reciprocal acoustic devices.

## Key findings

- Active Willis metamaterials enable non-reciprocal sound transport.
- Experimental extraction of effective material parameters is demonstrated.
- Active control surpasses passive limitations in Willis media.

## Abstract

Willis materials are complex media characterized by four macroscopic material parameters, the conventional mass density, and bulk modulus and two additional Willis coupling terms, which have been shown to enable unsurpassed control over the propagation of mechanical waves. However, virtually all previous studies on Willis materials involved passive structures which have been shown to have limitations in terms of achievable Willis coupling terms. In this article, we show experimentally that linear active Willis metamaterials breaking these constraints enable highly non-reciprocal sound transport in very subwavelength structures, a feature unachievable through other methods. Furthermore, we present an experimental procedure to extract the effective material parameters expressed in terms of acoustic polarizabilities for media in which the Willis coupling terms are allowed to vary independently. The approach presented here will enable a new generation of Willis materials for enhanced sound control and improved acoustic imaging and signal processing.